class Solution {
public:
    string multiply(string num1, string num2) {
        int n1 = num1.size(), n2 = num2.size();
        reverse(num1.begin(), num1.end());
        reverse(num2.begin(), num2.end());
        vector<int> tmp(n1 + n2);
        string ret;

        for (int i = 0; i < n1; i++) {
            for (int j = 0; j < n2; j++) {
                tmp[i + j] += (num1[i] - '0') * (num2[j] - '0');
            }
        }

        int cur = 0, t = 0;
        while (cur < n1 + n2 - 1 || t != 0) {
            if (cur < n1 + n2 - 1) t += tmp[cur++];
            ret += t % 10 + '0';
            t /= 10;
        }

        while (ret.size() > 1 && ret.back() == '0') ret.pop_back();

        reverse(ret.begin(), ret.end());
        return ret;
    }
};